Counter-current heat exchangers are important elements of many heat engines and heat pumps. Typically, a counter-current heat exchanger is used in such systems to transfer heat from a stream of working fluid at one pressure to a stream at another pressure. In many refrigeration systems, for example, a warm stream coming from a compressor and a cold stream returning to the compressor pass through a heat exchanger in opposite directions. The warm stream gradually cools as it flows along the length of the exchanger due to its loss of heat to the cooler returning stream.
The efficiency of heat engines and heat pumps is limited largely by the degree of thermodynamic irreversibility in the heat transfer process of their counter-current heat exchangers. For example, in refrigeration systems using a single-component refrigerant, the heat capacity of the refrigerant may change significantly as its temperature and pressure changes. Consequently, as heat is transferred between the streams along the length of the heat exchanger, the temperature change of the high-pressure stream will be different from the temperature change of the low-pressure stream, causing the temperatures of the streams to diverge at one end of the heat exchanger. Since the degree of irreversibility of a heat exchange process increases as the temperature difference increases, this temperature divergence significantly increases the inefficiency of the refrigerator. More generally, in any heat pump or heat engine having a counter-current heat exchanger, the variation in the heat capacity of its working fluid imposes a theoretical limitation on its efficiency.
It is now known that these limitations on the efficiency of counter-current heat exchange processes can be minimized in theory by using multi-component working fluids. Components of the working fluid and their relative fractions can be chosen, in principle, so that the heat capacity of the working fluid at high pressure is equal to its heat capacity at low pressure over the entire temperature range of the heat exchanger. Consequently, the temperature difference between the two fluids will remain constant throughout the length of the heat exchanger and the efficiency of the system will be maximized.
The effective heat capacity of such a multi-component working fluid is defined as (dH/dT).sub.P, that is, the change in enthalpy of the mixture per unit change in temperature at constant pressure. Because the heat exchange between the high and low pressure streams may cause the components of the working fluid to change phase, the effective heat capacity of the mixture includes both contributions due to the heat capacities of the individual phases present in the mixture and contributions due to changes of phase in the mixture. In the following discussion, the effective heat capacity of a mixture is often referred to as simply the heat capacity of the mixture.
The first to recognize the theoretical possibility of maximizing heat-exchange efficiency through the use of multi-component working fluids was A. P. Kleemenko in his studies of single-stream, throttle-expansion cycle cryogenic refrigeration systems described in "One Flow Cascade Cycle," Proceedings of the Xth International Congress on Refrigeration, Copenhagen, 1, 34-39, (1959), Pergamon Press, London. It has subsequently been referred to in recent texts on cryogenic systems, such as "Theory and Design of Cryogenic Systems" by A. Arkjarov, I. Marfenina and Ye. Mikulin, Mir Publishers, Moscow (1981).
In the course of attempts to realize this theoretical possibility in cryogenic refrigeration systems, some specific mixed-gas refrigerants have been found that provide some improved refrigeration efficiency. Most notable are those refrigerant mixtures containing a mixture of nitrogen with some of the lighter hydrocarbon gases, such as methane, ethane, propane, and iso-butane. Similar mixtures containing, in addition, some of the Freons have been described by Alfeev, Brodyansky, Yagodin, Nikolsky & Ivantsov, British Patent 1,336,892 (1973); W. A. Little, Proceedings of the 5th Cryocooler Conference, Monterey, (1988); W. A. Little, Advances in Cryogenic Engineering, 1305-1314 (1990); C. K. Chan, Proceedings of Interagency Cryocooler Meeting on Cryocoolers, p.121 (1988), and R. Longsworth, U.S. Pat. No. 5,337,572 (1994). In comparison with single-component refrigerants, these refrigerant mixtures have smaller differences between the heat capacities of their high and low pressure streams over the wide temperature range needed for cryogenic operation. Consequently, they reduce the thermodynamic irreversibility in the heat exchange processes and improve the refrigeration efficiency.
The mixtures described in the prior art, however, still fall short of producing the maximum possible refrigeration efficiency. Since there are significant differences in the heat capacities of their low and high pressure streams, these mixtures--just like the single-component refrigerants--produce a temperature divergence in the counter-current heat exchanger. This divergence, in turn, increases the irreversibility and inefficiency of the heat-exchange process. Thus, in spite of the fact that many specific refrigeration mixtures have been proposed and used for obtaining improved efficiency, none comes close to obtaining the maximum possible efficiency.
In addition to thermodynamic efficiency, the performance of heat exchange processes is also determined in large part by the heat transfer capacity of the mixture over the operational temperature range. The difference in enthalpy between the high and low pressure streams determines the amount of heat that can be transferred between them. In order to provide refrigeration at cryogenic temperatures, for example, it is crucial that the heat transfer capacity of the mixture be significant over the entire operational temperature range. Many of the mixtures in the prior art, however, have increasingly reduced refrigeration capacity at lower temperatures. Consequently, the refrigerator performance with these mixtures decreases dramatically at low temperatures, and eventually reaches a low-temperature limit below which the mixture is unable to provide any refrigeration.
An attempt to develop a procedure for the optimization of refrigeration mixtures is described in Gorbachov, et al, "High Temperature Superconductivity", All-Union Scientific and Research Institute for Interdisciplinary Information, Vol. 3-4, Moscow (1990), p. 3-7, and in Boyarsky et al, "Properties of Cryogenic Systems working on Mixtures," Moscow Institute of Energy, Moscow (1990). This article proposes a complicated algorithm for the selection of the refrigerant mixture, based on the properties of the pure components. This procedure, however, is intended to yield a mixture with optimized refrigeration capacity, and it does not present a condition for optimizing refrigeration efficiency, i.e., for ensuring equality of the heat capacities of the two streams.
The prior art, therefore, does not teach any general procedure by which the composition of a refrigerant mixture can be adjusted or selected to produce a refrigeration system with both optimum thermodynamic efficiency and optimum refrigeration capacity. Thus, in spite of the fact that it has been theoretically possible and highly desirable since Kleemenko's discovery in 1959 to produce a maximally efficient refrigeration system through the use of a multiple-component mixture, the practical realization of such a highly efficient refrigerator has continued to elude researchers. In addition, no prior art provides a general or particular method for producing a heat engine or heat pump of any kind whose counter-current heat exchanger obtains or approaches minimal irreversibility through the use of an appropriately chosen refrigerant mixture.